Question

a jar contains 3 white marbles, 6 orange marbles, 4 yellow marbles, and 5 black marbles. if a marble is drawn at random, find the probability that the marble is either orange or yellow. what is the probability that the marble is orange or yellow (simplify your answer. type an integer or a fraction.)

Explanation:

Step1: Calculate total number of marbles

First, we find the total number of marbles by adding the number of each color. The number of white marbles is 3, orange is 6, yellow is 4, and black is 5. So total marbles \( n = 3 + 6 + 4 + 5 \).
\( n = 18 \)

Step2: Calculate number of orange or yellow marbles

The number of orange marbles is 6 and yellow is 4. Since we want either orange or yellow, we add these two numbers. Let \( m \) be the number of orange or yellow marbles. So \( m = 6 + 4 \).
\( m = 10 \)

Step3: Calculate probability

Probability \( P \) of an event is the number of favorable outcomes divided by total number of outcomes. So \( P=\frac{m}{n} \). Substituting \( m = 10 \) and \( n = 18 \), we get \( P=\frac{10}{18} \), which simplifies to \( \frac{5}{9} \).

Answer:

\(\frac{5}{9}\)